How to fix a 6 point vertex
There are some great resources out there (non-specific to Blender) about how to solve these kinds of problems. I'd recommend looking for some facial modeling tutes that talk about topology specifically.

To answer your question, though, you will have to have a tri or a 5-point vertex :-/ It's a veritable law of facial modeling and there's great debate (apparently) on where the unavoidable tris and 5's should go.

In this case, you'll probably want to make a face out of those three vertices you have circled, to make a tri. This will give you an edge loop that goes around the mouth, which is highly desirable. The debate usually surrounds how far away from the lips that tri should be. It's usually helpful to put the tri somewhere that it will mostly be flat, and won't distort very much. If it's small enough, it might not matter.